Transients of deformation at nanoscale observed in displacement controlled nanoindentation testing

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1 Transients of deformation at nanoscale observed in displacement controlled nanoindentation testing Ude D. Hangen Hysitron Inc., Gottfried Hagen Strasse 60, Köln, Germany Abstract As it comes to nanoscale it is observed that the materials properties are changing. This is found for electrical properties, optical properties and also mechanical properties. NanoIndentation testing [1] has been used to investigate the transients of deformation in displacement control [2] on Aluminium and PMMA. It can be shown that the deformation of crystalline materials at this scale exhibit discrete steps of deformation. This allows studying the energies needed for the deformation. Examples of standard nanoindentation tests at ambient as well as in-situ observations of deformation in the TEM will be presented. 1. Testing of Al <100> in displacement control Indentation experiments in literature are mostly performed in load control. A diamond pyramid (Vickers: fourfold symmetry; Berkovich: threefold symmetry) is pushed into a material using the force F. The tested material has a certain hardness H IT which is defined as H IT =F/A. A, the projected contact area, increases as the indentation depth h c increases: A=24.5h 2 c in the ideal case for a Berkovich indenter. The indentation experiment under load control is controlled by a constant hardness i.e. the increase in force is balanced by the increase in contact area. While load controlled indentation experiments are relatively easy to control and good for determining a hardness or modulus they do not allow studying the discrete nature of deformation of materials. In load control the instrument is ready to maintain the load applied which effectively means that the system is ready to use as much (deformation) energy as necessary to maintain the constant force. In the case of discrete yielding or slip plane phenomena as well as for fracture events the deformation occurs in sudden uncontrolled displacement excursions. As it comes to studying deformation mechanisms of materials the better instrument is capable of performing displacement controlled experiments. The current benchmark instrument allows a displacement control with a feedback loop speed of 73kHz and a noisefloor for the force of 30nN and displacement of 0.2nm. For this experiment a single crystal of Al with <100> orientation is electropolished to remove the deformation layer generated by cutting and grinding. A thin natural oxide layer is present on the surface. A TI-950 instrument from Hysitron, Inc. is used to perform the mechanical test. Figure 1 shows the force displacement curve. The yielding of the Al-crystal occurs as soon as a critical stress is reached under the indenter. The Fig. 1. Force-Displacement Curve on Al <100>. first loading up to approximately 18µN 4-282

2 is believed being pure elastic loading to generate the necessary critical stress for homogenous dislocation nucleation and first onset of plasticity. Since nanoindentation at this initial small depth is probing a very small volume of the crystal it is more likely to test an area without dislocation. A maximum force reached is followed by a load drop to a portion of the initial load. This indicates that the surface relaxes as soon as the dislocations start to move. The further deformation appears to be easier but still a load drop is followed by an increase in force until a critical stress level is reached again. The elastic stress that is build up in the Alcrystal is released during the next load drop and another discrete step of deformation is observed. 2. Indentation of Al in TEM A similar sample has been tested with a PI-95 indenter for TEM microscopes. A 150nm Al-coating has been deposited on a Si-wedge with a width of 150nm. Both the Si and the Al are electron-transparent in the TEM but the structure is also stable enough to allow mechanical testing. A Berkovich Geometry is used for the mechanical test. Fig. 2. (a) Al film deposited on a Silicon Substrate with a wedge; the Al is electron-transparent; (b) Sample mount in TEM; Sample: blue; Indenter from right hand side [3]. A single grain of Al was probed in the TEM experiment in a JEOL 3010 ) [3] which hence can be understood as being a confined single crystalline volume. The micrograph in Fig. 3 shows that the single crystal tested is indeed defect free and that the stress necessary for deformation hence should reach values that are closed to the theoretical yield stress. Figure 3 shows some image frames grabbed during the indentation experiments. It is observed that the Al-crysal has a first significant loading to a force of closed to 20µN followed by a load drop which is very much comparable to Fig. 1. In standard indentation this stage is believed of being only a pure elastic loading. When closely observing Fig. 3 small force signals are observed before the sample is going into the repulsive contact. These small force signals coincide with some significant changes going on in the Al grain. Micrograph 1 shows no initial contrast and is therefore believed to be defect and deformation free. After that Micrograph 2 and 3 show significant increase in contrast which reflects an increase in dislocation density i.e. deformation has occurred already. The direct observation of deformation also indicates that the deformation process is confined by the grain boundaries. The finding contradicts theoretical models that are assuming a pure elastic deformation of the sample until a critical stress has been reached. These models are used to calculate the 4-283

3 theoretical strength of the material tested. Here dislocation generation is shown. This mechanism actually strengthens the Al-grain and makes the modeling of the initial loading behavior of indenters more complex. Finally it might well be that the strength of the materials is increased due to the deformation in a confined volume and a very high strength closed to the theoretical strength is reached again. Fig. 3. Indentation experiment on a thin Al-film in a Jeol 3010 TEM; the micrographs show three stages of the experiment; these stages are identified in the Load-displacement curves [3]. 3. Concurrent measurements of force, displacement and current A nanoindenter equipped with a conductive boron-doped diamond can be used to study the conductivity of the sample while performing indentation experiments. Therefore a bias voltage is applied between the tip and the sample and the current flowing through the tip is recorded. An indentation test with a Cube Corner indenter on Al <100> is shown in Fig. 4. This indentation has been performed under load-control conditions and the force displacement signal (black curve) therefore shows a very smooth behavior. No load drops are observed (alike Fig. 1 and 3) where the tests were performed in displacement control. Interestingly this time the discontinuous behavior is observed on the current signal (red curve). While the current steps are very much pronounced, distinct non-continuous transients of deformation can barely be identified. This is a result of testing Al in load control. It has been shown earlier [4] that the current is related to the contact area between indenter and sample. The origin of the stepwise increase in current density therefore can give more insight into the development of the contact area between the Al crystal and the diamond indenter and is therefore under further investigation. Since Aluminium does not change its electrical properties due to deformation this finding suggests that the contact area develops in steps. The oxide layer on the material in its way of giving path to the electrons can play a role for this as well as pile-up or sink-in deformation of the Al <100>

4 Fig. 4. In-situ image of Al-indent without hint for discontinuous deformation; Force & Current recorded vs. displacement. 4. Use of load and displacement control when testing polymers When testing soft and visco-elastic materials a test in displacement control allows determining materials properties as stress-relaxation, load-controlled experiments allow testing the creep of a material. Even when tested at larger scale rheological experiments are performed in a displacement controlled mode because soft materials can never balance the forces applied. Visco-elastic material can be described by applying a sudden strain/displacement or by applying a sudden stress/load. This so called step loading needs a fast feedback control and data acquisition rate. The resulting experimental data can be fitted with a series of Maxwell elements of spring and dashpot in order to extract the materials characteristics from the curves. Figure 5 shows a experimental curve on PMMA with a step loading in 0.1s to a load of 100µN. The curve describes the displacement of the indenter tip in time after the load step. The red curve represents a fit with a Maxwell dashpot model with 2 elements. These elements have a time constant of t 1 and t 2. Hence the relationship describing the creep in this time frame is: t0 t t t0 t t 1 2 h( t) A1 e A2 e h( t0) h is the displacement, t the time and and t 0 is the time at the end of the step loading. In this example the deformation is described by the time constants t 1 =0.5s, t 2 =4.4s. Fig. 5. Stress-Relaxation in an indentation experiment. This type of analysis is very valuable in polymer applications; it is not only the glass transition that limits the use of polymers for certain applications but also the softening of the polymer

5 5. Summary The accurate control of experiments at the nanoscale is key to proper modeling and understanding the deformation behavior of materials. A very good control of either force or displacement allows analyzing the mechanisms underlying the plasticity in the nm regime. Indentation or scratch testing of hard or soft materials cannot be described with one mechanism but a very accurate control of the experiment is necessary in all cases. References 1. ISO Metallic Materials Instrumented Indentation Test for Hardness and Materials Parameters. 2. Warren, Downs, Wyrobek, Z. Metallkd. 2004, 95, A.M. Minor et al. Nature Mater. 2006, 5, Y.V. Sharvin. Sov. Phys. JETP. 1965, 21,